576 research outputs found
Ab-initio solution of the many-electron Schrödinger equation with deep neural networks
Given access to accurate solutions of the many-electron Schr\"odinger equation, nearly all chemistry could be derived from first principles. Exact wavefunctions of interesting chemical systems are out of reach because they are NP-hard to compute in general, but approximations can be found using polynomially-scaling algorithms. The key challenge for many of these algorithms is the choice of wavefunction approximation, or Ansatz, which must trade off between efficiency and accuracy. Neural networks have shown impressive power as accurate practical function approximators and promise as a compact wavefunction Ansatz for spin systems, but problems in electronic structure require wavefunctions that obey Fermi-Dirac statistics. Here we introduce a novel deep learning architecture, the Fermionic Neural Network, as a powerful wavefunction Ansatz for many-electron systems. The Fermionic Neural Network is able to achieve accuracy beyond other variational quantum Monte Carlo Ans\"atze on a variety of atoms and small molecules. Using no data other than atomic positions and charges, we predict the dissociation curves of the nitrogen molecule and hydrogen chain, two challenging strongly-correlated systems, to significantly higher accuracy than the coupled cluster method, widely considered the most accurate scalable method for quantum chemistry at equilibrium geometry. This demonstrates that deep neural networks can improve the accuracy of variational quantum Monte Carlo to the point where it outperforms other ab-initio quantum chemistry methods, opening the possibility of accurate direct optimisation of wavefunctions for previously intractable molecules and solids
Ab-initio quantum chemistry with neural-network wavefunctions
Machine learning and specifically deep-learning methods have outperformed
human capabilities in many pattern recognition and data processing problems, in
game playing, and now also play an increasingly important role in scientific
discovery. A key application of machine learning in the molecular sciences is
to learn potential energy surfaces or force fields from ab-initio solutions of
the electronic Schr\"odinger equation using datasets obtained with density
functional theory, coupled cluster, or other quantum chemistry methods. Here we
review a recent and complementary approach: using machine learning to aid the
direct solution of quantum chemistry problems from first principles.
Specifically, we focus on quantum Monte Carlo (QMC) methods that use neural
network ansatz functions in order to solve the electronic Schr\"odinger
equation, both in first and second quantization, computing ground and excited
states, and generalizing over multiple nuclear configurations. Compared to
existing quantum chemistry methods, these new deep QMC methods have the
potential to generate highly accurate solutions of the Schr\"odinger equation
at relatively modest computational cost.Comment: review, 17 pages, 6 figure
Solution of Schrödinger Equation for Quantum Systems via Physics-Informed Neural Networks
openThe numerous successes achieved by machine learning techniques in many technical areas have sparked interest in the scientific community for their application in science. By merging the knowledge of machine learning experts and computational scientists, the field of scientific machine learning has shown its ability to greatly improve the performance of existing computational methods. One possible approach to developing physics-aware machine learning is the inclusion of physical constraints in the training of a machine learning model. Physics-Informed Neural Networks are an example of such an approach, as they can incorporate prior physical knowledge into their architecture, enabling them to learn and simulate complex phenomena while respecting the underlying physics principles. Possible constraints are physical laws, symmetries, and conservation laws. Compared to other machine learning models, Physics-Informed Neural Networks do not require substantial input data, with the exception of initial and boundary conditions to correctly formalize the problem.
In this Thesis, we exploit the advantages of Physics-Informed Neural Networks to efficiently simulate one-electron quantum systems. The simulations rely on the direct solution of the eigenvalue equation represented by the Schrödinger equation. Traditional methods for solving the Schrödinger equation often rely on approximations and can become computationally expensive for nontrivial systems. The mesh-free Physics-Informed Neural Networks approach avoids the need for discretization, as the residuals computed with respect to the physical constraints are minimized during training for a given set of points within the domain.
The solution of the Schrödinger equation allows one to calculate important physical quantities of the physical system under study, such as the ground state energy, the electronic wavefunction, and the associated electron density. These quantities are compared with the estimations present in the quantum chemistry literature to assess the performance of the Physics-Informed Machine Learning approach.The numerous successes achieved by machine learning techniques in many technical areas have sparked interest in the scientific community for their application in science. By merging the knowledge of machine learning experts and computational scientists, the field of scientific machine learning has shown its ability to greatly improve the performance of existing computational methods. One possible approach to developing physics-aware machine learning is the inclusion of physical constraints in the training of a machine learning model. Physics-Informed Neural Networks are an example of such an approach, as they can incorporate prior physical knowledge into their architecture, enabling them to learn and simulate complex phenomena while respecting the underlying physics principles. Possible constraints are physical laws, symmetries, and conservation laws. Compared to other machine learning models, Physics-Informed Neural Networks do not require substantial input data, with the exception of initial and boundary conditions to correctly formalize the problem.
In this Thesis, we exploit the advantages of Physics-Informed Neural Networks to efficiently simulate one-electron quantum systems. The simulations rely on the direct solution of the eigenvalue equation represented by the Schrödinger equation. Traditional methods for solving the Schrödinger equation often rely on approximations and can become computationally expensive for nontrivial systems. The mesh-free Physics-Informed Neural Networks approach avoids the need for discretization, as the residuals computed with respect to the physical constraints are minimized during training for a given set of points within the domain.
The solution of the Schrödinger equation allows one to calculate important physical quantities of the physical system under study, such as the ground state energy, the electronic wavefunction, and the associated electron density. These quantities are compared with the estimations present in the quantum chemistry literature to assess the performance of the Physics-Informed Machine Learning approach
Variational Monte Carlo on a Budget -- Fine-tuning pre-trained Neural Wavefunctions
Obtaining accurate solutions to the Schr\"odinger equation is the key
challenge in computational quantum chemistry. Deep-learning-based Variational
Monte Carlo (DL-VMC) has recently outperformed conventional approaches in terms
of accuracy, but only at large computational cost. Whereas in many domains
models are trained once and subsequently applied for inference, accurate DL-VMC
so far requires a full optimization for every new problem instance, consuming
thousands of GPUhs even for small molecules. We instead propose a DL-VMC model
which has been pre-trained using self-supervised wavefunction optimization on a
large and chemically diverse set of molecules. Applying this model to new
molecules without any optimization, yields wavefunctions and absolute energies
that outperform established methods such as CCSD(T)-2Z. To obtain accurate
relative energies, only few fine-tuning steps of this base model are required.
We accomplish this with a fully end-to-end machine-learned model, consisting of
an improved geometry embedding architecture and an existing SE(3)-equivariant
model to represent molecular orbitals. Combining this architecture with
continuous sampling of geometries, we improve zero-shot accuracy by two orders
of magnitude compared to the state of the art. We extensively evaluate the
accuracy, scalability and limitations of our base model on a wide variety of
test systems
Electronic excited states in deep variational Monte Carlo
Obtaining accurate ground and low-lying excited states of electronic systems is crucial in a multitude of important applications. One ab initio method for solving the Schrödinger equation that scales favorably for large systems is variational quantum Monte Carlo (QMC). The recently introduced deep QMC approach uses ansatzes represented by deep neural networks and generates nearly exact ground-state solutions for molecules containing up to a few dozen electrons, with the potential to scale to much larger systems where other highly accurate methods are not feasible. In this paper, we extend one such ansatz (PauliNet) to compute electronic excited states. We demonstrate our method on various small atoms and molecules and consistently achieve high accuracy for low-lying states. To highlight the method’s potential, we compute the first excited state of the much larger benzene molecule, as well as the conical intersection of ethylene, with PauliNet matching results of more expensive high-level methods
Sampling-free Inference for Ab-Initio Potential Energy Surface Networks
Recently, it has been shown that neural networks not only approximate the
ground-state wave functions of a single molecular system well but can also
generalize to multiple geometries. While such generalization significantly
speeds up training, each energy evaluation still requires Monte Carlo
integration which limits the evaluation to a few geometries. In this work, we
address the inference shortcomings by proposing the Potential learning from
ab-initio Networks (PlaNet) framework, in which we simultaneously train a
surrogate model in addition to the neural wave function. At inference time, the
surrogate avoids expensive Monte-Carlo integration by directly estimating the
energy, accelerating the process from hours to milliseconds. In this way, we
can accurately model high-resolution multi-dimensional energy surfaces for
larger systems that previously were unobtainable via neural wave functions.
Finally, we explore an additional inductive bias by introducing
physically-motivated restricted neural wave function models. We implement such
a function with several additional improvements in the new PESNet++ model. In
our experimental evaluation, PlaNet accelerates inference by 7 orders of
magnitude for larger molecules like ethanol while preserving accuracy. Compared
to previous energy surface networks, PESNet++ reduces energy errors by up to
74%
Wasserstein Quantum Monte Carlo: A Novel Approach for Solving the Quantum Many-Body Schr\"odinger Equation
Solving the quantum many-body Schr\"odinger equation is a fundamental and
challenging problem in the fields of quantum physics, quantum chemistry, and
material sciences. One of the common computational approaches to this problem
is Quantum Variational Monte Carlo (QVMC), in which ground-state solutions are
obtained by minimizing the energy of the system within a restricted family of
parameterized wave functions. Deep learning methods partially address the
limitations of traditional QVMC by representing a rich family of wave functions
in terms of neural networks. However, the optimization objective in QVMC
remains notoriously hard to minimize and requires second-order optimization
methods such as natural gradient. In this paper, we first reformulate energy
functional minimization in the space of Born distributions corresponding to
particle-permutation (anti-)symmetric wave functions, rather than the space of
wave functions. We then interpret QVMC as the Fisher--Rao gradient flow in this
distributional space, followed by a projection step onto the variational
manifold. This perspective provides us with a principled framework to derive
new QMC algorithms, by endowing the distributional space with better metrics,
and following the projected gradient flow induced by those metrics. More
specifically, we propose "Wasserstein Quantum Monte Carlo" (WQMC), which uses
the gradient flow induced by the Wasserstein metric, rather than Fisher--Rao
metric, and corresponds to transporting the probability mass, rather than
teleporting it. We demonstrate empirically that the dynamics of WQMC results in
faster convergence to the ground state of molecular systems
A Non-stochastic Optimization Algorithm for Neural-network Quantum States
Neural-network quantum states (NQS) employ artificial neural networks to
encode many-body wave functions in second quantization through variational
Monte Carlo (VMC). They have recently been applied to accurately describe
electronic wave functions of molecules and have shown the challenges in
efficiency comparing with traditional quantum chemistry methods. Here we
introduce a general non-stochastic optimization algorithm for NQS in chemical
systems, which deterministically generates a selected set of important
configurations simultaneously with energy evaluation of NQS. This method
bypasses the need for Markov-chain Monte Carlo within the VMC framework,
thereby accelerating the entire optimization process. Furthermore, this
newly-developed non-stochastic optimization algorithm for NQS offers comparable
or superior accuracy compared to its stochastic counterpart and ensures more
stable convergence. The application of this model to test molecules exhibiting
strong electron correlations provides further insight into the performance of
NQS in chemical systems and opens avenues for future enhancements.Comment: 30 pages, 7 figures, and 1 tabl
- …